Abstract
In the present note, we study slant and hemislant submanifolds of an LP-cosymplectic manifold which are totally umbilical. We prove that every totally umbilical proper slant submanifold M of an LP-cosymplectic manifold (M) over bar is either totally geodesic or if M is not totally geodesic in (M) over bar then we derive a formula for slant angle of M. Also, we obtain the integrability conditions of the distributions of a hemi-slant submanifold, and then we give a result on its classification.